I have always had a soft spot for Gunning and Rossi ("Analytic Functions of Several Complex Variables"), probably because it is more "algebraic" in its approach) (sheaves, local rings, and so on. Hormander's "Introduction to Complex Analysis in Several Variables" takes what I always thought was a more "analytic" approach. I had it as a text in a course on SCV. Given your background, I might suggest Gunning-Rossi first. I have been out of touch with this area for some time. I'm sure there are more "modern" texts out there that would be fine for your purposes. Perhaps another responder could steer you toward them. I know there is a book by Stephen Krantz, for instance, but have no first-hand knowledge of it.